Do you want color, or to stick with something more plain like sisal?

I would do nothing smaller than a 5 x 7. 6 x 9 is even better.

from what I see a rug would not be my first direction for warmering the room.

attention to the windows would far more help the mood and the 'feeling' in this space. Color on the wall is a thought as well

the sun room furniture, need to weather the storm, no doubt. so I suggest findinf colorful rug which has the fabirc tone ( off white in it) You have the freedom at this point to choose any direction. So, find a rug, post it (better yet find a few). Once the rug is selected then we will move to the wall and windows.

If you just STICK as rug on the floor there will be little change to the mood in this space as the floor is the darkest warmest part

Good morning Gary...the lighter one may be too pastel.

you may be right lol lets keep it light!

I'm not sure how much color I want. The slate floor has a lot of different colors in it and its cold. Thank you for your comments!

check out your posted images of the floor.....the floor may have many tones, but only one overall tone....

Squint your eye....(mostly closed) study the rug, what you come up with is the 'tone' to work with for the rug, dont let the slate guide the way 100% or you will have a mouti colored slate colored rug and that wont help at all.

Or if you want this look-sorta of a more quiet look...but I like that sometimes.